Yes. You can get life insurance on that person as long as you have an insurable interest in that person’s life. That means that if that person were to pass away, it would cause financial distress. For example, a business can take out life insurance on an employee. This is called key man insurance.
Another example would be a spouse taking out insurance for the other spouse.
In general, the other party must agree to this policy being put in to effect as they must cooperate and sign off on the policy.